Blaschke's asymptotic lines of surfaces in R3

Abstract

In this paper we consider the Blaschke's asymptotic lines (also called affine asymptotic lines) of regular surfaces in 3-space. We study the binary differential equations defining Blaschke's asymptotic lines in the elliptic and hyperbolic regions of the surface near affine cusp points and to at affine umbilic points. We also describe the affine asymptotic lines near the Euclidean parabolic set including the Euclidean flat umbilic points.